precisely p.354. The related idea of stackification via torsors is also included. The result you mention seems to be only shown there for gerbes, though. I have no idea if this is the first occurrence of the idea, probably not.

I have heard this result attributed to Kai Behrend, who apparently came up with it while writing his part of the now defunct many-authored stack book. However it is certainly possible that someone else had already noticed it.

Really, that recently? I thought this was an old result. Certainly I hadn't seen it in the drafts of said book, or at least I hadn't read it in enough detail to see it.
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David RobertsAug 30 '11 at 9:17